Precision Measurement of the (e[superscript +] +
e[superscript ) Flux in Primary Cosmic Rays from 0.5 GeV
to 1 TeV with the Alpha Magnetic Spectrometer on the
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Citation
Aguilar, M., D. Aisa, B. Alpat, A. Alvino, G. Ambrosi, K. Andeen,
L. Arruda, et al. “Precision Measurement of the (e[superscript +]
+ e[superscript ) Flux in Primary Cosmic Rays from 0.5 GeV to 1
TeV with the Alpha Magnetic Spectrometer on the International
Space Station.” Physical Review Letters 113, no. 22 (November
2014). © 2014 American Physical Society
As Published
http://dx.doi.org/10.1103/PhysRevLett.113.221102
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American Physical Society
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Final published version
Accessed
Thu May 26 07:22:15 EDT 2016
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http://hdl.handle.net/1721.1/92240
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Detailed Terms
PRL 113, 221102 (2014)
PHYSICAL REVIEW LETTERS
week ending
28 NOVEMBER 2014
Precision Measurement of the ðeþ þ e− Þ Flux in Primary Cosmic Rays from 0.5 GeV to
1 TeV with the Alpha Magnetic Spectrometer on the International Space Station
M. Aguilar,26 D. Aisa,33,34 B. Alpat,33 A. Alvino,33 G. Ambrosi,33 K. Andeen,22 L. Arruda,24 N. Attig,21 P. Azzarello,33,16,a
A. Bachlechner,1 F. Barao,24 A. Barrau,17 L. Barrin,15 A. Bartoloni,38 L. Basara,3,37 M. Battarbee,44 R. Battiston,37,b
J. Bazo,33 U. Becker,9 M. Behlmann,9 B. Beischer,1 J. Berdugo,26 B. Bertucci,33,34 G. Bigongiari,35,36 V. Bindi,19
S. Bizzaglia,33 M. Bizzarri,33,34 G. Boella,28,29 W. de Boer,22 K. Bollweg,20 V. Bonnivard,17 B. Borgia,38,39 S. Borsini,33
M. J. Boschini,28 M. Bourquin,16 J. Burger,9 F. Cadoux,16 X. D. Cai,9 M. Capell,9 S. Caroff,3 J. Casaus,26 V. Cascioli,33
G. Castellini,14 I. Cernuda,26 F. Cervelli,35 M. J. Chae,40 Y. H. Chang,10 A. I. Chen,9 H. Chen,9 G. M. Cheng,6 H. S. Chen,6
L. Cheng,41 A. Chikanian,32,* H. Y. Chou,10 E. Choumilov,9 V. Choutko,9 C. H. Chung,1 C. Clark,20 R. Clavero,23
G. Coignet,3 C. Consolandi,19 A. Contin,7,8 C. Corti,19 B. Coste,37 M. Crispoltoni,33,34 Z. Cui,41 M. Dai,5 C. Delgado,26
S. Della Torre,28 M. B. Demirköz,2 L. Derome,17 S. Di Falco,35 L. Di Masso,33,34 F. Dimiccoli,37 C. Díaz,26
P. von Doetinchem,19 F. Donnini,33,34 W. J. Du,41 M. Duranti,33 D. D’Urso,33 A. Eline,9 F. J. Eppling,9 T. Eronen,44
Y. Y. Fan,43,c L. Farnesini,33 J. Feng,3,d E. Fiandrini,33,34 A. Fiasson,3 E. Finch,32 P. Fisher,9 Y. Galaktionov,9
G. Gallucci,35,15 B. García,26 R. García-López,23 C. Gargiulo,15 H. Gast,1 I. Gebauer,22 M. Gervasi,28,29 A. Ghelfi,17
W. Gillard,10 F. Giovacchini,26 P. Goglov,9 J. Gong,31 C. Goy,3 V. Grabski,27 D. Grandi,28 M. Graziani,33,15 C. Guandalini,7,8
I. Guerri,35,36 K. H. Guo,18 M. Habiby,16 S. Haino,10,43 K. C. Han,25 Z. H. He,18 M. Heil,9 J. Hoffman,10 T. H. Hsieh,9
Z. C. Huang,18 C. Huh,13 M. Incagli,35 M. Ionica,33 W. Y. Jang,13 H. Jinchi,25 K. Kanishev,37 G. N. Kim,13 K. S. Kim,13
Th. Kirn,1 R. Kossakowski,3 O. Kounina,9 A. Kounine,9 V. Koutsenko,9 M. S. Krafczyk,9 S. Kunz,22 G. La Vacca,28,15
E. Laudi,33,34,e G. Laurenti,7,8 I. Lazzizzera,37 A. Lebedev,9 H. T. Lee,43 S. C. Lee,43 C. Leluc,16 H. L. Li,43,f J. Q. Li,31
Q. Li,31 Q. Li,9,g T. X. Li,18 W. Li,4 Y. Li,16,d Z. H. Li,6 Z. Y. Li,43,d S. Lim,40 C. H. Lin,43 P. Lipari,38 T. Lippert,21 D. Liu,43
H. Liu,31 T. Lomtadze,35 M. J. Lu,37,h Y. S. Lu,6 K. Luebelsmeyer,1 F. Luo,41 J. Z. Luo,31 S. S. Lv,18 R. Majka,32
A. Malinin,12 C. Mañá,26 J. Marín,26 T. Martin,20 G. Martínez,26 N. Masi,7,8 D. Maurin,17 A. Menchaca-Rocha,27 Q. Meng,31
D. C. Mo,18 L. Morescalchi,35,i P. Mott,20 M. Müller,1 J. Q. Ni,18 N. Nikonov,22 F. Nozzoli,33 P. Nunes,24 A. Obermeier,1
A. Oliva,26 M. Orcinha,24 F. Palmonari,7,8 C. Palomares,26 M. Paniccia,16 A. Papi,33 M. Pauluzzi,33,34 E. Pedreschi,35
S. Pensotti,28,29 R. Pereira,24,19 F. Pilo,35 A. Piluso,33,34 C. Pizzolotto,33 V. Plyaskin,9 M. Pohl,16 V. Poireau,3 E. Postaci,2
A. Putze,3 L. Quadrani,7,8 X. M. Qi,18 T. Räihä,1 P. G. Rancoita,28 D. Rapin,16 J. S. Ricol,17 I. Rodríguez,26 S. Rosier-Lees,3
A. Rozhkov,9 D. Rozza,28 R. Sagdeev,11 J. Sandweiss,32 P. Saouter,16 C. Sbarra,7,8 S. Schael,1 S. M. Schmidt,21
D. Schuckardt,22 A. Schulz von Dratzig,1 G. Schwering,1 G. Scolieri,33 E. S. Seo,12 B. S. Shan,4 Y. H. Shan,4 J. Y. Shi,31
X. Y. Shi,9,j Y. M. Shi,42 T. Siedenburg,1 D. Son,13 F. Spada,38 F. Spinella,35 W. Sun,9 W. H. Sun,9,k M. Tacconi,28,29
C. P. Tang,18 X. W. Tang,6 Z. C. Tang,6 L. Tao,3 D. Tescaro,23 Samuel C. C. Ting,9 S. M. Ting,9 N. Tomassetti,17 J. Torsti,44
C. Türkoğlu,2 T. Urban,20 V. Vagelli,22 E. Valente,38,39 C. Vannini,35 E. Valtonen,44 S. Vaurynovich,9 M. Vecchi,3
M. Velasco,26 J. P. Vialle,3 L. Q. Wang,41 Q. L. Wang,5 R. S. Wang,42 X. Wang,9 Z. X. Wang,18 Z. L. Weng,9 K. Whitman,19
J. Wienkenhöver,1 H. Wu,31 X. Xia,26,f M. Xie,9,g S. Xie,42 R. Q. Xiong,31 G. M. Xin,41 N. S. Xu,18 W. Xu,6,9 Q. Yan,6
J. Yang,40 M. Yang,6 Q. H. Ye,42 H. Yi,31 Y. J. Yu,5 Z. Q. Yu,6 S. Zeissler,22 J. H. Zhang,31 M. T. Zhang,18 X. B. Zhang,18
Z. Zhang,18 Z. M. Zheng,4 H. L. Zhuang,6 V. Zhukov,1 A. Zichichi,7,8 N. Zimmermann,1 P. Zuccon,9 C. Zurbach30
(AMS Collaboration)
1
I. Physics Institute and JARA-FAME, RWTH Aachen University, D–52056 Aachen, Germany
2
Department of Physics, Middle East Technical University (METU), 06800 Ankara, Turkey
3
Laboratoire d’Annecy–Le–Vieux de Physique des Particules (LAPP), IN2P3/CNRS and Université de Savoie,
F–74941 Annecy–le–Vieux, France
4
Beihang University (BUAA), Beijing 100191, China
5
Institute of Electrical Engineering (IEE), Chinese Academy of Sciences, Beijing 100080, China
6
Institute of High Energy Physics (IHEP), Chinese Academy of Sciences, Beijing 100039, China
7
INFN Sezione di Bologna, I–40126 Bologna, Italy
8
Università di Bologna, I–40126 Bologna, Italy
9
Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, USA
10
National Central University (NCU), Chung–Li, Tao Yuan 32054, Taiwan
11
East–West Center for Space Science, University of Maryland, College Park, Maryland 20742, USA
12
IPST, University of Maryland, College Park, Maryland 20742, USA
0031-9007=14=113(22)=221102(7)
221102-1
© 2014 American Physical Society
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PHYSICAL REVIEW LETTERS
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13
CHEP, Kyungpook National University, 702–701 Daegu, Korea
14
CNR–IROE, I-50125 Firenze, Italy
15
European Organization for Nuclear Research (CERN), CH–1211 Geneva 23, Switzerland
16
DPNC, Université de Genève, CH–1211 Genève 4, Switzerland
17
Laboratoire de Physique Subatomique et de Cosmologie (LPSC), CNRS/IN2P3 and Université Grenoble–Alpes,
F–38026 Grenoble, France
18
Sun Yat–Sen University (SYSU), Guangzhou 510275, China
19
Physics and Astronomy Department, University of Hawaii, 2505 Correa Road, WAT 432, Honolulu, Hawaii 96822, USA
20
National Aeronautics and Space Administration Johnson Space Center (JSC), and Jacobs-Sverdrup, Houston, Texas 77058, USA
21
Jülich Supercomputing Centre and JARA-FAME, Research Centre Jülich, D–52425 Jülich, Germany
22
Institut für Experimentelle Kernphysik, Karlsruhe Institute of Technology (KIT), D–76128 Karlsruhe, Germany
23
Instituto de Astrofísica de Canarias (IAC), E–38205 La Laguna, Tenerife, Spain
24
Laboratório de Instrumentação e Física Experimental de Partículas, (LIP), P–1000 Lisboa, Portugal
25
National Chung–Shan Institute of Science and Technology (NCSIST), Longtan, Tao Yuan 325, Taiwan
26
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), E–28040 Madrid, Spain
27
Instituto de Física, Universidad Nacional Autónoma de México (UNAM), México D.F. 01000, Mexico
28
INFN Sezione di Milano–Bicocca, I–20126 Milano, Italy
29
Università di Milano–Bicocca, I–20126 Milano, Italy
30
Laboratoire Univers et Particules de Montpellier (LUPM), IN2P3/CNRS and Université de Montpellier II,
F–34095 Montpellier, France
31
Southeast University (SEU), Nanjing 210096, China
32
Physics Department, Yale University, New Haven, Connecticut 06520, USA
33
INFN Sezione di Perugia, I–06100 Perugia, Italy
34
Università di Perugia, I–06100 Perugia, Italy
35
INFN Sezione di Pisa, I–56100 Pisa, Italy
36
Università di Pisa, I–56100 Pisa, Italy
37
INFN TIFPA and Università di Trento, I–38123 Povo, Trento, Italy
38
INFN Sezione di Roma 1, I–00185 Roma, Italy
39
Università di Roma La Sapienza, I–00185 Roma, Italy
40
Department of Physics, Ewha Womans University, Seoul 120-750, Korea
41
Shandong University (SDU), Jinan, Shandong 250100, China
42
Shanghai Jiaotong University (SJTU), Shanghai 200030, China
43
Institute of Physics, Academia Sinica, Nankang, Taipei 11529, Taiwan
44
Space Research Laboratory, Department of Physics and Astronomy, University of Turku, FI–20014 Turku, Finland
(Received 5 September 2014; published 26 November 2014)
We present a measurement of the cosmic ray ðeþ þ e− Þ flux in the range 0.5 GeV to 1 TeV based on
the analysis of 10.6 million ðeþ þ e− Þ events collected by AMS. The statistics and the resolution of
AMS provide a precision measurement of the flux. The flux is smooth and reveals new and distinct
information. Above 30.2 GeV, the flux can be described by a single power law with a spectral index
γ ¼ −3.170 0.008ðstat þ systÞ 0.008ðenergy scaleÞ.
DOI: 10.1103/PhysRevLett.113.221102
PACS numbers: 96.50.sb, 95.35.+d, 95.85.Ry, 98.70.Sa
Measurements of cosmic rays by the Alpha Magnetic
Spectrometer (AMS) [1–3] of the positron fraction and the
positron flux Φðeþ Þ have been carried out up to 500 GeV
and of the electron flux Φðe− Þ up to 700 GeV. The results
generated widespread interest and discussions on the origin
of high-energy positrons and electrons [4]. They provide
information on the combined flux Φðeþ þ e− Þ up to
500 GeV. In this Letter we present a dedicated measurement of Φðeþ þ e− Þ up to 1 TeV with reduced statistical
and systematic errors.
AMS.—AMS is a general purpose high-energy particle
physics detector installed on the International Space Station
(ISS) to conduct a unique long-duration (∼20-yr) mission
of fundamental physics research in space [5]. It consists of a
tracker, a magnet, time of flight (TOF) and anticoincidence
counters, a ring imaging Čerenkov detector, an electromagnetic calorimeter (ECAL), and a transition radiation
detector (TRD).
The nine layer double-sided silicon microstrip tracker
accurately determines the trajectory and absolute charge jZj
of cosmic rays using multiple measurements of the coordinates and energy loss. Together with the 0.14 T permanent magnet, the tracker measures the particle rigidity
R ¼ p=Z, where p is the momentum. The maximum
detectable rigidity is 2 TV over a lever arm of 3 m.
The four TOF planes trigger the readout of all the
detectors and measure the particle velocity and direction.
The high efficiency (≃99.999%) anticoincidence counters
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PHYSICAL REVIEW LETTERS
inside the magnet bore are used to reject particles outside
the geometric acceptance. The tracker, TOF, and TRD
measure jZj independently. The curvature measured with
the tracker and the magnet and the direction of the particle
measured with the TOF yield the sign of the charge.
The 3-dimensional imaging capability of the 17 radiation
length (17X0 ) ECAL allows for an accurate measurement
of the ðeþ þ e− Þ energy E scaled to the top of AMS and
of the shower shape. An ECAL estimator, based on a
boosted decision tree algorithm [6], is used to differentiate
ðeþ þ e− Þ from protons by exploiting their different
shower shapes.
To further differentiate between ðeþ þ e− Þ and protons,
signals from the 20 layers of proportional tubes in the
TRD are combined into a TRD classifier formed from the
product of the probabilities of the ðeþ þ e− Þ hypothesis.
This TRD classifier has the same differentiation power as
the TRD likelihood variable used in [3] but has a different scale.
The timing, location, and attitude are determined by a
combination of GPS units affixed to AMS and to the ISS.
AMS operates continuously on the ISS and is monitored
and controlled around the clock from the ground. The
detector performance is steady over time.
The entire detector has been extensively calibrated in a
test beam at CERN with eþ and e− from 10 to 290 GeV=c,
with protons at 180 and 400 GeV=c, and with π from 10
to 180 GeV=c which produce transition radiation equivalent to protons up to 1.2 TeV=c. Measurements with 18
different energies and particles at 2000 positions were
performed. A Monte Carlo program based on the GEANT
4.9.4 package [7] is used to simulate physics processes and
detector signals.
Analysis.—Over 41 × 109 events collected from May 19,
2011, to November 26, 2013, have been analyzed. The
isotropic ðeþ þ e− Þ flux is measured in each energy bin E,
of width ΔE, as
Φðeþ þ e− Þ ¼
NðEÞ
Aeff ðEÞϵtrig ðEÞϵECAL ðEÞTðEÞΔE
week ending
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uncertainty of the absolute energy scale to 2% in the range
covered by the test beam results, 10–290 GeV. Below
10 GeV it increases to 5% at 0.5 GeVand above 290 GeV to
5% at 1 TeV. This is treated as an uncertainty on the bin
boundaries.
Events are selected requiring the presence of a downward-going, β > 0.83 particle which has hits in at least 8 of
the 20 TRD layers and a single track in the tracker passing
through the ECAL. Events with an energy deposition
compatible with a minimum ionizing particle in the first
5X0 of the ECAL are rejected. Events with jZj > 1 are
rejected using dE=dx in the tracker and TRD. Secondary
particles of atmospheric origin [8] are rejected with the
cutoff requirement discussed below.
In each energy bin, TRD classifier reference spectra of
the ðeþ þ e− Þ signal and the proton background are used as
templates. The templates are constructed from the data
using pure samples of e− and protons. These samples are
selected using the ECAL estimator, E=p matching, and the
charge sign. The templates are evaluated separately in each
bin; however, the signal templates show no dependence on
the energy above ∼10 GeV. Therefore, all the e− selected
in the range 15.1–83.4 GeV are taken as a unique signal
template up to the highest energies.
The sum of the signal and background templates is fit to
the data by varying their normalizations. This yields the
number of signal ðeþ þ e− Þ events N and the number of
background (proton) events. It also yields the statistical
errors on N and the number of background events. These
errors yield the statistical error on the flux. Figure 1
presents the data, the fit, and the signal and background
templates for one bin.
The effective detector acceptance is
Aeff ¼ Ageom ϵsel ð1 þ δÞ;
ð2Þ
where Ageom is the geometric acceptance, ϵsel is the event
selection efficiency, and δ is a data-derived correction. The
ð1Þ
where N is the number of ðeþ þ e− Þ events, Aeff is the
effective detector acceptance, ϵtrig is the trigger efficiency,
ϵECAL is the signal selection efficiency based on the ECAL
estimator, and T is the exposure time.
Equation (1) is evaluated independently in 74 energy
bins from 0.5 GeV to 1 TeV. The bin width is chosen to be
at least two times the energy resolution. The bin-to-bin
migration error is ∼1% at 1 GeV decreasing to 0.2% above
10 GeV. With increasing energy the bin width smoothly
increases to ensure adequate statistics in each bin.
The absolute energy scale is verified by using minimum
ionizing particles and the ratio E=p. These results are
compared with the test beam values where the beam energy
is known to high precision. This comparison limits the
FIG. 1 (color). The result of the template fit in the 149–
170 GeV bin showing the small proton background overlapping
the ðeþ þ e− Þ signal. The fit has a χ 2 =d:f: ¼ 0.55.
221102-3
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PHYSICAL REVIEW LETTERS
acceptance for a particle that passes through the active
volumes of the tracker, TRD, TOF, and ECAL is found to
be Ageom ≃ 550 cm2 sr and ϵsel has typical values of 90% at
10 GeV, 83% at 100 GeV, and 70% at 1 TeV. Both Ageom
and ϵsel are evaluated from the Monte Carlo simulation.
The small correction to the acceptance δ is estimated by
comparing the data and the Monte Carlo simulation
efficiencies for every selection cut using information from
the detectors unrelated to that cut. This correction is found
to be a smooth, slowly varying function of energy. It is
−0.04 at 2 GeV and −0.03 at 1 TeV.
The trigger efficiency is determined from data. The data
acquisition system is triggered by the coincidence of all
four TOF planes. AMS also records unbiased triggers
which require a coincidence of any three out of the four
TOF planes to measure ϵtrig . It is 100% above 3 GeV
decreasing to 75% at 1 GeV.
The ECAL estimator efficiency ϵECAL is measured from
the data using negative rigidity samples and the selection
cuts. ϵECAL values range from 75% to 95% for different
energy bins, depending on the number of signal and
background events.
The orbital parameters and the status of the detectors
are recorded for each second of data-taking. Live-time
weighted seconds are summed to obtain the exposure time
in a given energy bin only when the minimum bin energy
exceeds 1.2 times the maximum Størmer cutoff [9] for
jZj ¼ 1 particles in the AMS geometric acceptance. The
exposure time does not include time spent in the South
Atlantic Anomaly, time during TRD gas refills, and time
when the AMS z axis was more than 40° from the local
zenith. For the energy bins above ∼30 GeV, where the
effects of the geomagnetic cutoff are negligible, the
exposure time is 6.2 × 107 seconds. It decreases to
1.5 × 107 seconds at 5 GeV.
A total of 10.6 × 106 ðeþ þ e− Þ events have been
identified with energies from 0.5 GeV to 1 TeV. A major
experimental advantage of the combined flux analysis
compared to the measurement of the individual positron
and electron fluxes, particularly at high energies, is that
the selection does not depend on the charge sign. Another
advantage is that it has a higher overall efficiency.
Consequently, this measurement is extended to 1 TeV with
less overall uncertainty over the entire energy range.
Systematic uncertainties arise from (i) the event selection,
(ii) the acceptance, and (iii) bin-to-bin migration.
To evaluate the systematic uncertainty from the event
selection which includes the uncertainty from the construction of the templates, 2000 trials were performed in
each energy bin. Each trial consisted of the complete
analysis. The trials were performed with different values
of the ECAL estimator cut and different values of selection
cuts used to construct the templates. The 2000 trials are
performed in an interval of 5% in efficiency around the
value of the ECAL estimator cut which minimizes the
NE
PRL 113, 221102 (2014)
320
RMS = 4%
(b)
(a)
[500 - 700] GeV
300
20
18
16
260
14
12
10
240
8
6
220
4
280
200 150 100 50
Trials
0.78
0.8
0.82
0.84
0.86
∈ ECAL
2
0
FIG. 2 (color). For the 500–700 GeV bin: (a) N E versus ϵECAL
for the 2000 trials showing that the result is stable over a wide
range of ϵECAL . The scale on the right indicates the number of
trials. (b) The distribution of N E for the 2000 trials. The narrow
width (a rms of 4%) of the distribution indicates the accuracy at
the highest energies.
combined statistical and systematic uncertainties. For the
500–700 GeV bin, Fig. 2(a) shows the stability of the
number of signal events corrected by the ECAL estimator
selection efficiency N E ¼ N=ϵECAL as a function of ϵECAL .
As seen, N E does not depend on the efficiency and this was
found to be the case in every energy bin. Figure 2(b) shows
the distribution of N E for the 2000 trials in this bin. The
median value of the distribution determines the flux. The
rms spread of the distribution provides an evaluation of
the stability of the measurement. The difference between
the width of this distribution in data and the expected
statistical fluctuations quantifies the systematic uncertainty
as < 1% below ∼200 GeV increasing to 4% in the
500–700 GeV bin. This is the main source of systematic
uncertainty above ∼500 GeV.
The systematic error on the acceptance is given by the
uncertainty on δ. It is estimated from data to Monte Carlo
simulation comparisons. Above 3 GeV a systematic error
of 2% on ð1 þ δÞ is obtained from the contributions of all
the cuts. Below 3 GeV the uncertainty increases to 6% at
1 GeV. This is the major contribution to the systematic error
below ∼500 GeV. The systematic error on the acceptance
includes a bin-to-bin correlation of 1.4% over the entire
energy range.
Results.—The measured ðeþ þ e− Þ flux is presented in
Table I as a function of the energy at the top of AMS
together with its statistical and systematic errors, where the
systematic errors are the quadratic sum of the systematic
uncertainties listed above, (i)-(iii). The table also contains a
~ for a flux
representative value of the energy in the bin, E,
∝ E−3 [10] and the error on E~ according to the energy scale
uncertainty. Several independent analyses were performed
on the same data sample by different study groups. The
results of those analyses are consistent with the results
presented here. The flux multiplied by E~ 3 is presented in
Fig. 3, together with previous measurements [11–17].
Below ∼10 GeV, the behavior of Φðeþ þ e− Þ is affected
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PRL 113, 221102 (2014)
TABLE I. The electron plus positron flux Φðeþ þ e− Þ in units
of ½GeV · m2 · sr · s−1 with its statistical and systematic errors.
The systematic uncertainties include an overall scaling uncertainty of 1.4% which introduces a correlation between bins. E~ as
described in the text with its systematic error derived from the
energy scale uncertainty. The bin boundaries and E~ are the
energies at the top of AMS.
Energy (GeV)
0.50–0.65
0.65–0.82
0.82–1.01
1.01–1.22
1.22–1.46
1.46–1.72
1.72–2.00
2.00–2.31
2.31–2.65
2.65–3.00
3.00–3.36
3.36–3.73
3.73–4.12
4.12–4.54
4.54–5.00
5.00–5.49
5.49–6.00
6.00–6.54
6.54–7.10
7.10–7.69
7.69–8.30
8.30–8.95
8.95–9.62
9.62–10.32
10.3–11.0
11.0–11.8
11.8–12.6
12.6–13.4
13.4–14.2
14.2–15.1
15.1–16.1
16.1–17.0
17.0–18.0
18.0–19.0
19.0–20.0
20.0–21.1
21.1–22.2
22.2–23.4
23.4–24.6
24.6–25.9
25.9–27.2
27.2–28.7
28.7–30.2
30.2–31.8
31.8–33.5
33.5–35.4
35.4–37.3
37.3–39.4
39.4–41.6
41.6–44.0
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PHYSICAL REVIEW LETTERS
E~ (GeV)
Φðeþ þ e− Þ σ stat σ syst
0.57 0.03
0.73 0.03
0.91 0.04
1.11 0.05
1.33 0.05
1.58 0.06
1.85 0.07
2.15 0.08
2.47 0.08
2.82 0.09
3.17 0.10
3.54 0.11
3.92 0.12
4.32 0.12
4.76 0.13
5.24 0.14
5.74 0.15
6.26 0.15
6.81 0.16
7.39 0.17
7.99 0.18
8.62 0.19
9.28 0.19
9.96 0.20
10.7 0.2
11.4 0.2
12.2 0.2
13.0 0.3
13.8 0.3
14.7 0.3
15.6 0.3
16.5 0.3
17.5 0.3
18.5 0.4
19.5 0.4
20.6 0.4
21.7 0.4
22.8 0.5
24.0 0.5
25.2 0.5
26.6 0.5
28.0 0.6
29.4 0.6
31.0 0.6
32.7 0.7
34.4 0.7
36.3 0.7
38.3 0.8
40.5 0.8
42.8 0.9
ð2.71 0.10 0.54Þ × 10þ1
ð2.38 0.02 0.21Þ × 10þ1
ð2.17 0.01 0.16Þ × 10þ1
ð2.01 0.01 0.12Þ × 10þ1
ð1.78 0.01 0.09Þ × 10þ1
ð1.46 0.00 0.06Þ × 10þ1
ð1.19 0.00 0.04Þ × 10þ1
ð9.47 0.01 0.28Þ × 100
ð7.48 0.01 0.19Þ × 100
ð5.77 0.01 0.13Þ × 100
ð4.81 0.01 0.10Þ × 100
ð3.77 0.01 0.08Þ × 100
ð2.99 0.00 0.06Þ × 100
ð2.37 0.00 0.05Þ × 100
ð1.87 0.00 0.04Þ × 100
ð1.47 0.00 0.03Þ × 100
ð1.16 0.00 0.02Þ × 100
ð9.13 0.01 0.19Þ × 10−1
ð7.24 0.01 0.15Þ × 10−1
ð5.76 0.01 0.12Þ × 10−1
ð4.57 0.01 0.09Þ × 10−1
ð3.65 0.01 0.07Þ × 10−1
ð2.92 0.01 0.06Þ × 10−1
ð2.35 0.01 0.05Þ × 10−1
ð1.89 0.00 0.04Þ × 10−1
ð1.54 0.00 0.03Þ × 10−1
ð1.26 0.00 0.03Þ × 10−1
ð1.03 0.00 0.02Þ × 10−1
ð8.42 0.03 0.17Þ × 10−2
ð6.91 0.02 0.14Þ × 10−2
ð5.73 0.02 0.12Þ × 10−2
ð4.74 0.02 0.10Þ × 10−2
ð3.93 0.02 0.08Þ × 10−2
ð3.29 0.01 0.07Þ × 10−2
ð2.75 0.01 0.06Þ × 10−2
ð2.31 0.01 0.05Þ × 10−2
ð1.94 0.01 0.04Þ × 10−2
ð1.65 0.01 0.03Þ × 10−2
ð1.39 0.01 0.03Þ × 10−2
ð1.19 0.01 0.02Þ × 10−2
ð9.98 0.06 0.20Þ × 10−3
ð8.52 0.05 0.17Þ × 10−3
ð7.22 0.04 0.15Þ × 10−3
ð6.03 0.04 0.12Þ × 10−3
ð5.15 0.03 0.11Þ × 10−3
ð4.29 0.03 0.09Þ × 10−3
ð3.64 0.03 0.07Þ × 10−3
ð3.11 0.02 0.06Þ × 10−3
ð2.59 0.02 0.05Þ × 10−3
ð2.18 0.02 0.04Þ × 10−3
(Table continued)
TABLE I.
(Continued)
Energy (GeV)
44.0–46.6
46.6–49.3
49.3–52.3
52.3–55.6
55.6–59.1
59.1–63.0
63.0–67.3
67.3–72.0
72.0–77.4
77.4–83.4
83.4–90.2
90.2–98.1
98–107
107–118
118–132
132–149
149–170
170–198
198–237
237–290
290–370
370–500
500–700
700–1000
E~ (GeV)
Φðeþ þ e− Þ σ stat σ syst
45.3 0.9
47.9 1.0
50.8 1.0
53.9 1.1
57.3 1.1
61.0 1.2
65.1 1.3
69.6 1.4
74.6 1.5
80.3 1.6
86.7 1.7
94.0 1.9
103 2
113 2
125 3
140 3
159 3
183 4
216 4
262 5
327 7
429 13
589 22
832 38
ð1.81 0.02 0.04Þ × 10−3
ð1.49 0.01 0.03Þ × 10−3
ð1.24 0.01 0.03Þ × 10−3
ð1.04 0.01 0.02Þ × 10−3
ð8.62 0.10 0.18Þ × 10−4
ð7.06 0.09 0.15Þ × 10−4
ð5.62 0.07 0.12Þ × 10−4
ð4.56 0.06 0.09Þ × 10−4
ð3.66 0.05 0.08Þ × 10−4
ð2.91 0.04 0.06Þ × 10−4
ð2.32 0.04 0.05Þ × 10−4
ð1.78 0.03 0.04Þ × 10−4
ð1.37 0.03 0.03Þ × 10−4
ð1.01 0.02 0.02Þ × 10−4
ð7.26 0.15 0.15Þ × 10−5
ð5.04 0.12 0.11Þ × 10−5
ð3.55 0.09 0.08Þ × 10−5
ð2.17 0.06 0.05Þ × 10−5
ð1.27 0.04 0.03Þ × 10−5
ð6.89 0.27 0.16Þ × 10−6
ð3.45 0.17 0.09Þ × 10−6
ð1.45 0.10 0.04Þ × 10−6
ð5.41 0.56 0.23Þ × 10−7
ð1.90 0.40 0.23Þ × 10−7
by solar modulation. However, above 20 GeV the effects of
solar modulation are insignificant within the current experimental accuracy. The data show no structures. In particular, from 10 GeV to 1 TeV the flux is smooth and reveals
new and distinct information.
As seen in Fig. 3, the flux cannot be described by a single
power law (Φ ∝ Eγ ) over the entire range. To estimate a
lower energy limit above which a single power law
describes the flux, we use energy intervals with starting
energies from 0.5 GeV and increasing bin by bin. The
ending energy for all intervals is fixed at 1 TeV. Each
interval is split into two sections with a boundary between
the starting energy and 1 TeV. Each of the two sections is
fit with a single power law and we obtain two spectral
indices. The lowest starting energy of the interval that
gives consistent spectral indices at the 90% C.L. for any
boundary yields a lower limit of 30.2 GeV.
To quantitatively examine the energy dependence of the
flux in a model independent way, the flux is fit with a
spectral index γ as
Φðeþ þ e− Þ ¼ CEγ
or
γ ¼ d½logðΦÞ=d½logðEÞ
ð3Þ
(E in GeV and C is a normalization) over a sliding energy
window. The width of the window varies with energy to
have sufficient sensitivity to determine the spectral index.
The resulting energy dependence of the fitted spectral index
is shown in Fig. 4(a), where the shading indicates the
221102-5
3
E × Φ (GeV2 [ m2 sr sec ]-1)
PRL 113, 221102 (2014)
400
PHYSICAL REVIEW LETTERS
AMS-02
ATIC
BETS 97&98
PPB-BETS 04
Fermi-LAT
HEAT
H.E.S.S.
H.E.S.S. (LE)
350
300
250
200
150
100
50
0
1
10
10
2
10
3
Energy (GeV)
FIG. 3 (color). The flux of electrons plus positrons Φðeþ þ e− Þ
measured by AMS multiplied by E~ 3 versus energy. The AMS error
bars are the quadratic sum of the statistical and systematic errors.
Also shown are the results from earlier experiments [11–17].
Spectral Index
correlation between neighboring points due to the sliding
energy window. Fitting a single power law over the range
30.2 GeV to 1 TeV yields γ ¼ −3.170 0.008 0.008,
where the first error is the combined statistical and
systematic uncertainty and the second error is due to the
energy scale uncertainty. This is shown in Fig. 4(b).
It is important to note, as discussed in Ref. [3], that a
single power law can describe the electron flux above
52.3 GeV and a single power law, with a different spectral
index, can describe the positron flux above 27.2 GeV. The
simultaneous single power law behavior of Φðeþ Þ, Φðe− Þ,
and Φðeþ þ e− Þ is unexpected.
-2.2
-2.4
(a)
-2.6
-2.8
-3
-3.2
-3.4
-3.6
102
10
E3 × Φ (GeV2 [ m2 sr sec ]-1)
Energy (GeV)
250
200
(b)
Data
γ
Fit to C × E
150
100
50
0
102
103
Energy (GeV)
FIG. 4 (color). (a) The spectral index of Φðeþ þ e− Þ as a
function of energy. The shaded regions indicate the 68% C.L.
intervals including the correlation between neighboring points
due to the sliding energy window. (b) Φðeþ þ e− Þ multiplied by
E~ 3 versus energy and the result of a single power law fit above
30.2 GeV.
week ending
28 NOVEMBER 2014
This measurement of Φðeþ þ e− Þ together with the
measurements of Φðeþ Þ and Φðe− Þ [3] and the positron
fraction make possible the accurate comparison with
various particle physics and astrophysics models including
the minimal model discussed in Refs. [1,2]. This will be
presented in a separate publication.
In conclusion, the precision measurement of
Φðeþ þ e− Þ as a function of energy from 0.5 GeV to
1 TeV indicates that the flux is smooth and reveals new and
distinct information. No structures were observed. From
30.2 GeV to 1 TeV, the flux can be described by a single
power law with γ ¼ −3.170 0.008ðstat þ systÞ 0.008
ðenergyscaleÞ.
We thank former NASA Administrator Daniel S. Goldin
for his dedication to the legacy of the ISS as a scientific
laboratory and his decision for NASA to fly AMS as a DOE
payload. We also acknowledge the support of the NASA
leadership including Charles Bolden and William
Gerstenmeier. We are grateful for the support of Jim
Siegrist and Michael Salamon of the DOE. We also
acknowledge the continuous support from MIT and its
School of Science, Michael Sipser, Marc Kastner, Ernest
Moniz, and Richard Milner. Research supported by: CAS,
NNSF, MOST, NLAA, the provincial governments of
Shandong, Jiangsu, and Guangdong, and the China
Scholarship Council, China, including work at IHEP by
the National Natural Science Foundation; CNRS, IN2P3,
CNES, Enigmass, and the ANR, France including support
of M. Vecchi by CNES; J. Trümper, J.D. Woerner, and
DLR, Germany, including work at Aachen University and
KIT by the Deutsches Zentrum für Luft- und Raumfahrt
and computing resources from JARA-HPC under Project
No. JARA0052 for Aachen and Jülich; INFN and ASI,
Italy, including the work of J. Bazo, F. Nozzili, and C.
Pizzolotto at the ASI Science Data Center in the framework
of ASI-INFN Agreement No. C/011/11/1 and work at
INFN Sezioni di Bologna, Milano, Perugia, Pisa, Roma,
and Trento by the Italian Space Agency (ASI), Contract
No. ASI-INFN I/002/13/0; Grants No. NRF-2009-0080142
and No. NRF-2012-010226 at CHEP, Kyungpook National
University and Grant No. NRF-2013-004883 at Ewha
Womans University, Korea; the Consejo Nacional de
Ciencia y Tecnologa at UNAM, Mexico; CIEMAT,
CDTI, and, at CIEMAT, by SEIDI–MINECO, and
CPAN, Spain; the Swiss National Science Foundation
(SNSF), federal and cantonal authorities, Switzerland;
Academia Sinica and the National Science Council
(NSC), former President of Academia Sinica Yuan-Tseh
Lee and former Ministers of NSC, Maw-Kuen Wu and
Luo-Chuan Lee, Taiwan, including work at both NCU
and the Institute of Physics, Academia Sinica, by the
Ministry of Science and Technology; and the Turkish
Atomic Energy Authority at METU, Turkey. We gratefully
acknowledge the strong support from CERN, including
Rolf-Dieter Heuer, and from the European Space Agency.
221102-6
PRL 113, 221102 (2014)
PHYSICAL REVIEW LETTERS
We are grateful for important discussions with Barry
Barish, Jonathan Ellis, Jonathan Feng, Steve Olsen,
George Smoot, Michael Turner, Steven Weinberg, and
Frank Wilczek. The strong support of the JSC and
MSFC flight control teams has allowed AMS to operate
optimally on the ISS for over three years.
[5]
*
Deceased.
Currently at ISDC, CH–1290 Versoix, Switzerland.
b
Also at ASI, I–00133 Roma, Italy.
c
Also at Xi’an Jiaotong University (XJTU), Xi’an 710049,
China.
d
Also at Sun Yat–Sen University (SYSU), Guangzhou
510275, China.
e
Currently at European Organization for Nuclear Research
(CERN), CH–1211 Geneva 23, Switzerland.
f
Also at Shandong University (SDU), Jinan, Shandong
250100, China.
g
Also at Harbin Institute of Technology (HIT), Harbin
150001, China.
h
Also at University of Science and Technology of China
(USTC), Hefei 230026, China.
i
Also at Università di Siena, I–53100 Siena, Italy.
j
Also at Beijing Normal University (BNU), Beijing 100875,
China.
k
Also at Southeast University (SEU), Nanjing 210096,
China.
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